scholarly journals The fate of the axial anomaly in a finite field theory

2020 ◽  
Vol 35 (05) ◽  
pp. 2050025
Author(s):  
Pierre Grangé ◽  
Jean-François Mathiot ◽  
Ernst Werner
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Decay Amplitude ◽  
Vector Current ◽  
Leading Order ◽  
Axial Anomaly ◽  
Internal Loop ◽  
Lagrange Formulation ◽  
Dimensional Space Time

The conservation of the vector current and the axial anomaly responsible for the [Formula: see text] decay amplitude are obtained in leading order within the Taylor–Lagrange formulation of fields considered as operator-valued distributions. As for gauge theories, where this formulation eliminates all divergences and preserves gauge symmetry, it is shown that the different contributions can be evaluated directly in four-dimensional space–time, with no restrictions whatsoever on the four-momentum of the internal loop, and without the need to introduce any additional nonphysical degrees of freedom like Pauli–Villars fields. We comment on the similar contributions responsible for the decay of the Higgs boson into two photons.

scholarly journals Gravitational Theory Without the Cosmological Constant Problem

1997 ◽  
Vol 12 (32) ◽  
pp. 2421-2424 ◽  
Author(s):  
E. I. Guendelman ◽  
A. B. Kaganovich
Keyword(s):  
Cosmological Constant ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Realistic Model ◽  
Gravitational Theory ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time

We develop a gravitational theory where the measure of integration in the action principle is not necessarily [Formula: see text] but it is determined dynamically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of "non-gravitating vacuum energy" which states that the Lagrangian density L can be changed to L + const. without affecting the dynamics. Formulating the theory in the first-order formalism we get as a consequence of the variational principle a constraint that enforces the vanishing of the cosmological constant. The most realistic model that implements these ideas is realized in a six or higher dimensional space–time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that the remaining four-dimensional space–time must have effective zero cosmological constant.

scholarly journals ON UNITARITY OF A LINEARIZED YANG–MILLS FORMULATION FOR MASSLESS AND MASSIVE GRAVITY WITH PROPAGATING TORSION

2010 ◽  
Vol 25 (26) ◽  
pp. 4911-4932
Author(s):  
ROLANDO GAITAN DEVERAS
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Massive Gravity ◽  
Dynamical Variable ◽  
General Covariance ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Perturbative Regime ◽  
Massive Theory ◽  
Extended Theories

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang–Mills formulation for gravity in a (2+1)-dimensional space–time. In the massless case, we show that the theory contains three degrees of freedom and only one is a nonunitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert–Einstein–Fierz–Pauli unitary massive theory plus three massless modes, two of them represents nonunitary ones. Finally, we confirm the existence of a family of unitary Yang–Mills-extended theories which are classically consistent with Einstein's solutions coming from nonmassive and topologically massive gravity. The unitarity of these Yang–Mills-extended theories is shown in a perturbative regime. A possible way to perform a nonperturbative study is remarked.

ULTRAVIOLET FINITE GAUGE THEORIES IN THE FIVE-DIMENSIONAL SPACE-TIME

1993 ◽  
Vol 08 (35) ◽  
pp. 3345-3348
Author(s):  
V. V. BELOKUROV ◽  
M. Z. IOFA
Keyword(s):  
High Power ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Arbitrary Dimension ◽  
Space Time ◽  
Covariant Derivatives ◽  
Dimensional Space Time ◽  
The One

Ultraviolet divergencies in gauge theories including those with higher powers of covariant derivatives are discussed in a space-time of an arbitrary dimension. In particular, it is noted that in the case d=5 all the one-loop graphs are finite, and theories with sufficiently high power of derivatives are finite in all orders.

scholarly journals NON-RELATIVISTIC FERMIONS, COADJOINT ORBITS OF W∞ AND STRING FIELD THEORY AT c=1

1992 ◽  
Vol 07 (33) ◽  
pp. 3129-3145 ◽  
Author(s):  
AVINASH DHAR ◽  
GAUTAM MANDAL ◽  
SPENTA R. WADIA
Keyword(s):  
Dimensional Space ◽  
Space Distribution ◽  
One Dimension ◽  
Coadjoint Orbits ◽  
Leading Order ◽  
Weak Coupling Regime ◽  
Phase Space Distribution ◽  
Dimensional Space Time ◽  
Area Preserving ◽  
Geometric Formulation

We apply the method of coadjoint orbits of W∞-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space distribution of the Fermi fluid. The action has an infinite series of expansion in the string coupling, which to leading order reduces to the previously discussed geometric action for the classical Fermi fluid based on the group w∞ of area-preserving diffeomorphisms. We briefly discuss the strong coupling limit of the string theory which, unlike the weak coupling regime, does not seem to admit a two-dimensional space-time picture. Our methods are equally applicable to interacting fermions in one dimension.

Galilean covariant effective theory for bound states of heavy mesons

2018 ◽  
Vol 33 (30) ◽  
pp. 1850180
Author(s):  
L. M. Abreu ◽  
M. de Montigny ◽  
E. S. Santos ◽  
D. F. C. A. Silva
Keyword(s):  
Bound States ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Heavy Meson ◽  
Effective Theory ◽  
Heavy Mesons ◽  
Interaction Terms ◽  
Effective Lagrangian ◽  
Dimensional Space Time ◽  
Covariant Version

In this work we formulate the Galilei-covariant version of an effective theory containing nonrelativistic heavy mesons and pions as degrees of freedom. This manifestly Galilean covariant framework is based on a five-dimensional space–time that has been used in the description of covariant nonrelativistic physics. In this context, effective Lagrangian is introduced without ambiguities, containing kinetic and interaction terms that are naturally Galilean invariant. The leading-order scattering amplitudes and the properties of possible heavy-meson bound states are calculated and discussed.

Consistency and universality in odd and even dimensional space–time QFT perturbative calculations

2014 ◽  
Vol 29 (13) ◽  
pp. 1450068
Author(s):  
O. A. Battistel ◽  
G. Dallabona
Keyword(s):  
Extra Dimensions ◽  
Dimensional Space ◽  
Vector Current ◽  
Space Time ◽  
Time Dimension ◽  
Ward Identities ◽  
Feynman Integrals ◽  
Regularization Techniques ◽  
Dimensional Space Time ◽  
Vacuum Polarization Tensor

The questions related to the consistent interpretation of QFT perturbative amplitudes are considered in light of a novel procedure, alternative to the traditional ones based on regularization prescriptions. A detailed discussion about the aspects associated to the space–time dimension is performed. For this purpose, it is considered a simple model having a fermionic vector current, coupled to a vector field, as well as a fermionic scalar current, coupled to a scalar field, both of them composed by different species of massive fermions. The referred currents are related in a precise way, which is reflected in the Ward identities for the perturbative physical amplitudes. The double vector two-point fermionic function, related to the vacuum polarization tensor of QED, as well as the amplitudes related to such quantity through relations among Green functions are explicit evaluated in space–time dimensions d = 2, 3, 4, 5 and 6. In the adopted procedure the perturbative amplitudes are not modified in intermediary steps of the calculations, as occurs in regularization procedures. Divergent Feynman integrals are not really solved. They appear only in standard objects, conveniently defined, where no physical parameter is present. Only very general properties for such quantities are assumed. For the finite parts, a set of functions is introduced which allows universal forms for the results. We show that scale independent, ambiguity free amplitudes are automatically obtained in a regularization independent way. As a consequence, interesting and, in certain way, surprising aspects are revealed in a clear and transparent way when the Ward identities and low-energy limits are verified for the simple amplitudes considered in the presently reported investigation. The obtained results suggest that the procedure can be considered as an advantageous tool to handle with the problem of divergences in perturbative solutions of QFT's, relative to the traditional regularization techniques, since the obtained results are so consistent as desirable and there are no limitations of applicability. In particular, the method can be applied in odd and even space–time dimensions having extra dimensions, which is not possible within the context of traditional regularization.

scholarly journals ON THE POSSIBLE EXISTENCE OF NEW FERMIONIC DEGREES OF FREEDOM IN D = 6

2003 ◽  
Vol 8 (2) ◽  
pp. 155-164
Author(s):  
P. Miškinis
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Physical Object ◽  
Space Time ◽  
Dimensional Space Time ◽  
Fermionic Fields

The bispinors formed by quaternion in D = 6 dimensional space‐time are proposed to be treated as new fermionic fields. The gauge nonabelian field is formulated by the quaternions. A new kind of physical object, an extended relativistic quaternionic membrane in D = 6, is discussed.

COVARIANT QUANTIZATION OF MASSLESS SUPERPARTICLE IN 4-DIMENSIONAL SPACE-TIME: TWISTOR APPROACH

1989 ◽  
Vol 04 (19) ◽  
pp. 1827-1837 ◽  
Author(s):  
M.S. PLYUSHCHAY
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Space Time ◽  
Extended Model ◽  
Covariant Quantization ◽  
Covariant Operator ◽  
Dimensional Space Time ◽  
Penrose Twistor

With the help of Penrose twistor approach by introducing the auxiliary “Stückelberg” degrees of freedom, the “extended” model of massless superparticle is constructed in 4-dimensional space-time, which is equivalent to the original Brink-Schwarz model. The covariant operator quantization of the obtained system is performed in the cases of N=1 and extended supersymmetries. It is shown that there are three independent schemes of quantization of the system at even N, one of which becomes anomalous at odd N.

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